Mark Scheme (Results) January Pearson Edexcel Level 3 Award In Algebra (AAL30)

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1 Mark Scheme (Results) January 0 Pearson Edexcel Level 3 Award In Algebra (AAL30)

2 Edexcel and BTEC Qualifications Edexcel and BTEC qualifications are awarded by Pearson, the UK s largest awarding body. We provide a wide range of qualifications including academic, vocational, occupational and specific programmes for employers. For further information visit our qualifications websites at or Alternatively, you can get in touch with us using the details on our contact us page at Pearson: helping people progress, everywhere Pearson aspires to be the world s leading learning company. Our aim is to help everyone progress in their lives through education. We believe in every kind of learning, for all kinds of people, wherever they are in the world. We ve been involved in education for over 50 years, and by working across 70 countries, in 00 languages, we have built an international reputation for our commitment to high standards and raising achievement through innovation in education. Find out more about how we can help you and your students at: January 0 Publications Code EA03759 All the material in this publication is copyright Pearson Education Ltd 0

3 NOTES ON MARKING PRINCIPLES Types of mark M marks: method marks A marks: accuracy marks B marks: unconditional accuracy marks (independent of M marks) Abbreviations cao correct answer only isw ignore subsequent working oe or equivalent (and appropriate) indep - independent ft follow through SC: special case dep dependent 3 No working If no working is shown then correct answers normally score full marks If no working is shown then incorrect (even though nearly correct) answers score no marks. With working If there is a wrong answer indicated on the answer line always check the working in the body of the script (and on any diagrams), and award any marks appropriate from the mark scheme. If working is crossed out and still legible, then it should be given any appropriate marks, as long as it has not been replaced by alternative work. If it is clear from the working that the correct answer has been obtained from incorrect working, award 0 marks. If there is no answer on the answer line then check the working for an obvious answer. Any case of suspected misread loses A (and B) marks on that part, but can gain the M marks. Discuss each of these situations with your Team Leader. If there is a choice of methods shown, then no marks should be awarded, unless the answer on the answer line makes clear the method that has been used.

4 5 Follow through marks Follow through marks which involve a single stage calculation can be awarded without working since you can check the answer yourself, but if ambiguous do not award. Follow through marks which involve more than one stage of calculation can only be awarded on sight of the relevant working, even if it appears obvious that there is only one way you could get the answer given. 6 Ignoring subsequent work It is appropriate to ignore subsequent work when the additional work does not change the answer in a way that is inappropriate for the question: e.g. incorrect cancelling of a fraction that would otherwise be correct It is not appropriate to ignore subsequent work when the additional work essentially makes the answer incorrect e.g. algebra. Transcription errors occur when candidates present a correct answer in working, and write it incorrectly on the answer line; mark the correct answer. 7 Parts of questions Unless allowed by the mark scheme, the marks allocated to one part of the question CANNOT be awarded in another. 8 Use of ranges for answers If an answer is within a range this is inclusive, unless otherwise stated.

5 PAPER: AAL30_0 Question Working Answer Mark Notes (a) x 6 x 5 B cao (b) y + 3 y 5 B cao (c) v B cao (d) w w M for correct method for partial simplification w A for w (accept w ) (a) x 5 = 6y M for correct method to rearrange to 6y=x-5 or y= x+c 5 y = x A for oe 3 (b) y = 5x + 0 y = 5 x + c M for correct method to find gradient of line perpendicular to 5x + y = 0 A for y = 5 x + c oe 3 (a) a² a 3 M for 3 terms correct out of terms A cao (b) 3cd(3cd 8) B for 3cd(3cd 8) (B for a correct but not fully factorised expression) (c) 5(g h ) 5(g h)(g + h) B cao (B for correct linear factors)

6 PAPER: AAL30_0 Question Working Answer Mark Notes 3 M for correct first operation p + 5 = n = ± n p 5 A for (p + 5)n = or n = p 5 n = p 5 A for n = ± OR p 5 pn = 5n pn + 5n = (p + 5)n = n = p 5 5 a =, b = 6, c = 6 6 = = 8 = M for correct formula or M for 8 A for 3 5 oe 6 6 oe 6 Exponential Cubic Quadratic Circular Reciprocal 3 B3 cao (B for 3 or correct, B for or correct))

7 PAPER: AAL30_0 Question Working Answer Mark Notes M for correct method to combine the fractions M(dep) for full simplification of the numerator x(3x ) A for or or or x(3x ) x( 3 x) 3x x x 3x 8 shaded region 5 M for drawing line x = 3 M for drawing line 3x + y = 6 M for drawing line y = x + 5 A for fully correct region shaded (A for correct shading for one inequality) to M for using values 3,.5,, 0.7 to 0.8, 0.6, 0.5 (condone one error) M (dep) for substituting values into trapezium rule, eg ( 3 0.5) ( ) A for 5.55 to5.65

8 PAPER: AAL30_0 Question Working Answer Mark Notes 0 (a), M for correct method to factorise x² x A cao (b) (3p 5)(p + ) > 0 p <, p > M for factorising (3p 5)(p + ) A ft for establishing the critical values, 3 5 oe, A for p < (or) p > 3 5 (do not accept p < and p > 3 5 ) OR M for sketching y = 3p² + p 0 A ft for establishing the critical values, 3 5 oe, A for p < (or) p > 3 5 (do not accept p < and p > 3 5 ) (a) 3² a 0 a 6 9 M for use of discriminant, eg 3² a A for a 6 9 oe

9 PAPER: AAL30_0 Question Working Answer Mark Notes (b) b, 0 3 M for at least one correct equation = 6 6 A for b = c 5 A for c = 0 = 6 3 (a) (x + 3 ) 9 + (x + 3 ) 5 M for (x + 3 ) oe A for (x + 3 ) 5 oe (b) When x = 0, y = Sketch graph 3 B for general shape (parabola) B for minimum point in third quadrant B for y intercept labelled at (0, ) (c) ( 3, 5 ) B cao 3 Sketch graph x = and y = 0 (0, ) M for correct shape A for fully correct graph with one y intercept shown and not crossing the x axis B for equations of asymptotes x = and y = 0 B for (0, ) marked on the graph

10 PAPER: AAL30_0 Question Working Answer Mark Notes 8x + (x) = 3 x² = 3 x = x² =, y = M for eliminating one variable x= M for simplifying to get x = oe or y²=, y= A for x = oe, y = AND x = - oe, y = - x = ± y = ± (A for x = ± oe or y = ± or x = oe, y = or x = - oe, y = -) 5 (a) B cao (b) ( 3 )( + 3 ) = 3 M for correct method to expand A cao (c) M for multiplying both numerator and denominator by a suitable 3 6 expression, eg 3 or a multiple of 3 3 A oe where a and b are both integers 6

11 PAPER: AAL30_0 Question Working Answer Mark Notes 6 (a)(i) B cao (ii) 5 B cao (b) n ( + (n ) 5) n(5n ) OR M for stating or using S = n(a + (n )d) A ft for n(5n ) oe OR n ( + 5n 3) = n(5n ) M for stating or using S = n(a + l) and l = a+(n-)d A ft for n(5n ) oe 7 5 = k 3 3 k = V = x 3 3 M for V x 3 or V = kx 3 M for method to establish value of k A for V = x 3 8 circle drawn M for circle centre (0, 0) drawn A for circle centre (0, 0), radius 6 drawn

12 PAPER: AAL30_0 Question Working Answer Mark Notes 9 (a) Cubic graph drawn M for calculating points for values of x from x = 3 to +3 with at least correct values of y B for drawing suitable axes on grid for their points A for all points correct A for drawing smooth curve through the correct points (b).5, 0.,. Bft for all three values, accept values in the range.5 to.6, 0. to 0. and.3 to. (c)., 0.5,.6 M for equation written in the form 6x x 3 = x + or line y = x + drawn on graph or equation y= x+ seen A ft for all three values, accept values in the range. to.3, 0.5 to 0.6 and.6 to.7

13 PAPER: AAL30_0 Question Working Answer Mark Notes 0 (a) between 0 38 and 0 39 B for between 0 38 and 0 39 (accept in the first minute of the journey oe) (b) 60 0 M for attempt to find gradient by using a right angled triangle or using the formula or using or 0 A for 0 oe (c) 60 6 (6 + 38) M for attempt to find the area under the graph, eg (6 + 38) 0 M for complete and correct method A cao (SCB for 77 if no other marks awarded) 60 6, ±8 M for intention to multiply all terms by (0 x) or 9 9 (0 + x) or correct method to add and 0 x 0 x M for multiplying all terms by (0 x)(0 + x) oe M for correct method to clear brackets A cao

14 Q8 y x

15 Qb y O x

16 Q3 y O -½ x

17 Q9 y 8 y = x + y = x(6 x ) O 3 x - -8

18

19

20 Pearson Education Limited. Registered company number 8788 with its registered office at Edinburgh Gate, Harlow, Essex CM0 JE

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